NIMCET 2023 — Reasoning PYQ

Step-by-step Solution 
$\text{1.}$ Let the present age of Rakesh be $R$ and the present age of Mahesh be $M$. 
$\text{2.}$ A relationship between their ages is given by the statement: "Rakesh says to Mahesh – “I am as old as you were when I was one-third as you are”". This can be translated into an equation. [1, 2]  
$\text{3.}$ Let $x$ be the number of years ago when Rakesh's age was one-third of Mahesh's current age. At that time, Rakesh's age was $R-x$ and Mahesh's age was $M-x$. 
$\text{4.}$ According to the statement, Rakesh's age at that time was $\frac{1}{3}M$. So, $R-x=\frac{1}{3}M$. 
$\text{5.}$ The statement also says that Rakesh's current age is equal to Mahesh's age at that time. So, $R=M-x$. 
$\text{6.}$ From the equation $R=M-x$, it can be deduced that $x=M-R$. 
$\text{7.}$ Substitute the value of $x$ into the equation from step $\text{4}$: $R-(M-R)=\frac{1}{3}M$. 
$\text{8.}$ Simplify the equation: $2R-M=\frac{1}{3}M$. 
$\text{9.}$ Rearrange the terms to express $R$ in terms of $M$: $2R=M+\frac{1}{3}M=\frac{4}{3}M$. 
$\text{10.}$ Further simplify to find the relationship between $R$ and $M$: $R=\frac{2}{3}M$. 
$\text{11.}$ It is also given that the sum of their ages is $60$ years: $R+M=60$. 
$\text{12.}$ Substitute the expression for $R$ from step $\text{10}$ into the sum equation: $\frac{2}{3}M+M=60$. 
$\text{13.}$ Combine the terms involving $M$: $\frac{5}{3}M=60$. 
$\text{14.}$ Solve for $M$: $M=60\times \frac{3}{5}=12\times 3=36$. 
Final Answer 
The present age of Mahesh is $36$ years.